High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials

An energy-based model of the ferroelectric polarization process is presented in the current contribution. In an energy-based setting, dielectric displacement and strain (or displacement) are the primary independent unknowns. As an internal variable, the remanent polarization vector is chosen. The model is then governed by two constitutive functions: the free energy function and the dissipation function. Choices for both functions are given. As the dissipation function for rate-independent response is non-differentiable, it is proposed to regularize the problem. Then, a variational equation can be posed, which is subsequently discretized using conforming finite elements for each quantity. We point out which kind of continuity is needed for each field (displacement, dielectric displacement and remanent polarization) is necessary to obtain a conforming method, and provide corresponding finite elements. The elements are chosen such that Gauss' law of zero charges is satisfied exactly. The discretized variational equations are solved for all unknowns at once in a single Newton iteration. We present numerical examples gained in the open source software package Netgen/NGSolve

Exposure of zebra mussels to radial extracorporeal shock waves: implications for treatment of fracture nonunions

Background: Radial extracorporeal shock wave therapy (rESWT) is an attractive, non-invasive therapy option to manage fracture nonunions of superficial bones, with a reported success rate of approximately 75%. Using zebra mussels (Dreissena polymorpha), we recently demonstrated that induction of biomineralization after exposure to focused extracorporeal shock waves (fESWs) is not restricted to the region of direct energy transfer into calcified tissue. This study tested the hypothesis that radial extracorporeal shock waves (rESWs) also induce biomineralization in regions not directly exposed to the shock wave energy in zebra mussels. Methods: Zebra mussels were exposed on the left valve to 1000 rESWs at different air pressure (between 0 and 4 bar), followed by incubation in calcein solution for 24 h. Biomineralization was evaluated by investigating the fluorescence signal intensity found on sections of the left and right valves prepared two weeks after exposure. Results: General linear model analysis demonstrated statistically significant (p < 0.05) effects of the applied shock wave energy as well as of the side (left/exposed vs. right/unexposed) and the investigated region of the valve (at the position of exposure vs. positions at a distance to the exposure) on the mean fluorescence signal intensity values, as well as statistically significant combined energy × region and energy × side × region effects. The highest mean fluorescence signal intensity value was found next to the umbo, i.e., not at the position of direct exposure to rESWs. Conclusions: As in the application of fESWs, induction of biomineralization by exposure to rESWs may not be restricted to the region of direct energy transfer into calcified tissue. Furthermore, the results of this study may contribute to better understand why the application of higher energy flux densities beyond a certain threshold does not necessarily lead to higher success rates when treating fracture nonunions with extracorporeal shock wave therapy

Damage and Failure Prediction of Laminated Weaves by Mechanism Based Envelopes

Abweichender Titel laut Übersetzung der Verfasserin/des VerfassersDie Forderung nach immer effizienteren und leichteren Strukturen erhöht kontinuierlich den Einsatz von faserverstärkten Kunststoffen. Um deren gesamtes Potential nutzen zu können sind aussagekräftige Berechnugsmodelle notwendig. Diese Arbeit beschäftigt sich mit der Entwicklung eines Konzepts zur Beurteilung der Materialauslastung von Verbundwerkstoffen im Allgemeinen und Faser-Kunststoff-Verbundlaminaten aus biaxialen Geflechten im Speziellen. Es wird die Idee verfolgt, anhand einer Einheitszelle die Spannungen und Verzerrungen aus der linearen Finiten Elemente Analyse einer Struktur zu beurteilen.Als Grundlage dient die Verwendung der Finiten Elemente Methode. Durch eine aus Schalenelementen modellierte Einheitszelle ist es möglich effizient nichtlineare Effekte in den Faserbündeln und Matrixtaschen zu berücksichtigen. Zum Einsatz kommem Konstitutivgesetze die Schädigung und Plastizieren zulassen. Es werden skalare Größen definiert denen mechanismenbasierte dissipierte Energien zu Grunde liegen. Diese ermöglichen den Grad der Materialauslastung zu beschreiben. Mittels radialer Belastungspfade verteilt im ebenen Spannungsraum erfolgt zum Einen die Erstellung von Hüllflächen, die ein bestimmtes Niveau an Schädigung oder Plastizieren markieren. Zum Anderen wird die Vorhersage der Reihenfolge des Eintretens vordefinierter Ereignisse möglich.Abschließend wird eine Strategie entwickelt um den Grad der Materialauslastung in kritische und nicht kritische Zustände einzuteilen. Dabei bedient man sich der Steigung von Verläufen der dissipierten Energieniveaus.Als Grundlage dienen kraftgesteuerte Analysen. Wegen des nichtlinearen Verhaltens werden diese von den Ergebnissen aus verschiebungsgesteuerten Analysen abweichen. Zusätzlich ist zu betonen, dass die Verwendung anderer Materialgesetze zu abweichenden Resultaten führen kann. Beides ist in weiterführenden Arbeiten zu prüfen.7

Quantitative analysis of surface wave patterns of Min proteins

The Min protein system is arguably the best-studied model system for biological pattern formation. It exhibits pole-to-pole oscillations in E. coli bacteria as well as a variety of surface wave patterns in in vitro reconstitutions. Such Min surface wave patterns pose particular challenges to quantification as they are typically only semi-periodic and non-stationary. Here, we present a methodology for quantitatively analysing such Min patterns, aiming for reproducibility, user-independence, and easy usage. After introducing pattern-feature definitions and image-processing concepts, we present an analysis pipeline where we use autocorrelation analysis to extract global parameters such as the average spatial wavelength and oscillation period. Subsequently, we describe a method that uses flow-field analysis to extract local properties such as the wave propagation velocity. We provide descriptions on how to practically implement these quantification tools and provide Python code that can directly be used to perform analysis of Min patterns.BN/Cees Dekker La

Directing Min protein patterns with advective bulk flow

The Min proteins constitute the best-studied model system for pattern formation in cell biology. We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns for low MinE:MinD concentration ratios, upstream propagation for large ratios, but multistability of both propagation directions in between. Whereas downstream propagation can be described by a minimal model that disregards MinE conformational switching, upstream propagation can be reproduced by a reduced switch model, where increased MinD bulk concentrations on the upstream side promote protein attachment. Our study demonstrates that a differential flow, where bulk flow advects protein concentrations in the bulk, but not on the surface, can control surface-pattern propagation. This suggests that flow can be used to probe molecular features and to constrain mathematical models for pattern-forming systems.</p

Stress-controlled decomposition routes in cubic AlCrN films assessed by in-situ high-temperature high-energy grazing incidence transmission X-ray diffraction

The dependence of decomposition routes on intrinsic microstructure and stress in nanocrystalline transition metal nitrides is not yet fully understood. In this contribution, three Al0.7Cr0.3N thin films with residual stress magnitudes of −3510, −4660 and −5930 MPa in the as-deposited state were in-situ characterized in the range of 25–1100 °C using in-situ synchrotron high-temperature high-energy grazing-incidence-transmission X-ray diffraction and temperature evolutions of phases, coefficients of thermal expansion, structural defects, texture as well as residual, thermal and intrinsic stresses were evaluated. The multi-parameter experimental data indicate a complex intrinsic stress and phase changes governed by a microstructure recovery and phase transformations taking place above the deposition temperature. Though the decomposition temperatures of metastable cubic Al0.7Cr0.3N phase in the range of 698–914 °C are inversely proportional to the magnitudes of deposition temperatures, the decomposition process itself starts at the same stress level of ~−4300 MPa in all three films. This phenomenon indicates that the particular compressive stress level functions as an energy threshold at which the diffusion driven formation of hexagonal Al(Cr)N phase is initiated, provided sufficient temperature is applied. In summary, the unique synchrotron experimental setup indicated that residual stresses play a decisive role in the decomposition routes of nanocrystalline transition metal nitrides

Directing Min protein patterns with advective bulk flow

The Min proteins constitute the best-studied model system for pattern formation in cell biology. We theoretically predict and experimentally show that the propagation direction of in vitro Min protein patterns can be controlled by a hydrodynamic flow of the bulk solution. We find downstream propagation of Min wave patterns for low MinE:MinD concentration ratios, upstream propagation for large ratios, but multistability of both propagation directions in between. Whereas downstream propagation can be described by a minimal model that disregards MinE conformational switching, upstream propagation can be reproduced by a reduced switch model, where increased MinD bulk concentrations on the upstream side promote protein attachment. Our study demonstrates that a differential flow, where bulk flow advects protein concentrations in the bulk, but not on the surface, can control surface-pattern propagation. This suggests that flow can be used to probe molecular features and to constrain mathematical models for pattern-forming systems.BN/Cees Dekker La